In the thesis I offer an analysis of the metaphysical underpinnings of the extended cognition thesis via an examination of standard views of metaphysical building (or, dependence) relations. -/- In summary form, the extended cognition thesis is a view put forth in naturalistic philosophy of mind stating that the physical basis of cognitive processes and cognitive processing may, in the right circumstances, be distributed across neural, bodily, and environmental vehicles. As such, the extended cognition thesis breaks substantially with the still (...) widely held view in cognitive science and philosophy of mind, namely that cognitive processes and cognitive processing take place within the skin-and-skull of individual organisms. The standard view of metaphysical building relations can be expressed as the conjunction of two theses. First, that a metaphysical building relation – such as composition, constitution, realization, supervenience or emergence – is a relation of ontological dependence, because if a metaphysical building relation holds between X (or the Xs) and Y, then it is in virtue of X (or the Xs) that Y exists. Second, metaphysical building relations are synchronic (durationless) relations of ontological dependence. In the thesis, I propose an alternative diachronic framework by which to extend the standard synchronic accounts of metaphysical dependence relations, and by which to reformulate the metaphysical foundation of the extended cognition thesis. The project fills an important gap between analytical metaphysics (in particular, the metaphysics of dependence relations) and naturalistic philosophy of mind (especially the extended cognition thesis). To my knowledge there has been no attempt to establish a robust diachronic account of metaphysical building (or, dependence) relations such as, e.g., composition and constitution. However, this is precisely what I argue is required to properly advance and ground the metaphysics of extended cognition. Ultimately, my aim of reformulating the metaphysics of extended cognition consists in taking several steps toward a third-wave of extended cognition. (shrink)